Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 9 - Polar Coordinates; Vectors - 9.5 The Dot Product - 9.5 Assess Your Understanding - Page 615: 19



Work Step by Step

By definition the dot product of 2 vector $ai+bj$ and $ci+dj$ is: $(ai+bj)(ci+dj)=ac+bd.$ If this product is 0, then the vectors are orthogonal (perpendicular) and hence the enclosed angle is $90^\circ.$ Hence here $v\cdot w=(i-aj)(2i+3j)=1\cdot2+(-a)\cdot3=0.$ We get the equation: $2-3a=0$, hence $a=\frac{2}{3}$.
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